The equivalence of centro-equiaffine curves

SAĞIROĞLU Y., Peksen O.

TURKISH JOURNAL OF MATHEMATICS, vol.34, no.1, pp.95-104, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 1
  • Publication Date: 2010
  • Doi Number: 10.3906/mat-0810-25
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.95-104
  • Karadeniz Technical University Affiliated: Yes

Abstract

The motivation of this paper is to find formulation of the SL(n, R)-equivalence of curves. The types for centro-equiaffine curves and for every type all invariant parametrizations for such curves are introduced. The problem of SL(n, R)-equivalence of centro-equiaffine curves is reduced to that of paths. The centro-equiaffine curvatures of path as a generating system of the differential ring of SL(n, R)-invariant differential polinomial functions of path are found. Global conditions of SL(n,R)-equivalence of curves are given in terms of the types and invariants. It is proved that the invariants are independent.